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kennethreitz/pytheory.ipynb

Created February 19, 2019 11:23
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pytheory.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "pytheory.ipynb",
"version": "0.3.2",
"provenance": [],
"collapsed_sections": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"metadata": {
"id": "_EMGkCYzn9UY",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"# A Premier on PyTheory\n",
"\n",
"PyTheory is a music theory library, which procedurally generates all known Western tones, scales, and chord fingering charts (for custom fretboards).\n",
"\n",
"It is capable of outputting either a rounded decimal for pitch representation, or the *proper* symbolic representation of the pitch (as a SymPy object).\n",
"\n",
"\n",
"## Install PyTheory:"
]
},
{
"metadata": {
"id": "4OwiDe7_oF9s",
"colab_type": "code",
"outputId": "c39a192a-eaac-497a-b3d4-3ef286a56fab",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 187
}
},
"cell_type": "code",
"source": [
"!pip install pytheory"
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"Requirement already satisfied: pytheory in /usr/local/lib/python3.6/dist-packages (0.1.1)\n",
"Requirement already satisfied: pygame in /usr/local/lib/python3.6/dist-packages (from pytheory) (1.9.4)\n",
"Requirement already satisfied: pytuning in /usr/local/lib/python3.6/dist-packages (from pytheory) (0.7.2)\n",
"Requirement already satisfied: numeral in /usr/local/lib/python3.6/dist-packages (from pytheory) (0.1.0.11)\n",
"Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from pytheory) (1.1.0)\n",
"Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from pytuning->pytheory) (1.14.6)\n",
"Requirement already satisfied: sympy in /usr/local/lib/python3.6/dist-packages (from pytuning->pytheory) (1.1.1)\n",
"Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy->pytuning->pytheory) (1.1.0)\n"
],
"name": "stdout"
}
]
},
{
"metadata": {
"id": "c1duUNkKoGOA",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"## Import PyTheory:"
]
},
{
"metadata": {
"id": "LVzQLkRtoGge",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"from pytheory import TonedScale"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "VZQzVX0UoG7f",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"Let's reference a great key (and the only one I can play on piano), A Minor:\n"
]
},
{
"metadata": {
"id": "asUQar6roHRR",
"colab_type": "code",
"outputId": "2e5a027e-2ec8-4cb5-f8ad-112368cfef49",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 35
}
},
"cell_type": "code",
"source": [
"a_min = TonedScale(tonic=\"A4\")[\"minor\"]\n",
"a_min"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<Scale I=A4 II=B4 III=C4 IV=D4 V=E4 VI=F4 VII=G4 VIII=A5>"
]
},
"metadata": {
"tags": []
},
"execution_count": 3
}
]
},
{
"metadata": {
"id": "oSmNsjmSogOt",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"Let's reference another great key, C Major:"
]
},
{
"metadata": {
"id": "O6O7pr1jogdh",
"colab_type": "code",
"outputId": "26fee874-ed48-400a-f473-249b415a759d",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 35
}
},
"cell_type": "code",
"source": [
"c_maj = TonedScale(tonic=\"C4\")[\"major\"]\n",
"c_maj"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<Scale I=C4 II=D4 III=E4 IV=F4 V=G4 VI=A5 VII=B5 VIII=C5>"
]
},
"metadata": {
"tags": []
},
"execution_count": 4
}
]
},
{
"metadata": {
"id": "8HUSLP8Qpx5J",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"That's interesting, they contain all the same notes! \n",
"\n",
"----------------\n",
"\n",
"Let's see if we can automatically detect what the modal correspondents are to A Minor:"
]
},
{
"metadata": {
"id": "l9IuJHlWqQoQ",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
"from pytheory import SYSTEMS\n",
"\n",
"def get_scale(tonic, mode):\n",
" return TonedScale(tonic=tonic)[mode]\n",
"\n",
"def get_all_scales(octave=4): \n",
" scales = []\n",
" \n",
" # Iterate over all 12 tones of the Western system: \n",
" for tone in SYSTEMS[\"western\"].tones:\n",
" \n",
" # Create a scale for each tone.\n",
" new_scale = TonedScale(tonic=f\"{tone.name}{octave}\")\n",
" \n",
" for mode in new_scale._scales.keys():\n",
" # Create every possible permutation of the scale. \n",
" newest_scale = TonedScale(tonic=f\"{tone.name}{octave}\")[mode]\n",
" \n",
" # (tone, mode, scale) tuple. \n",
" scales.append((tone, mode, newest_scale))\n",
" \n",
" return scales\n",
"\n",
"\n",
"def get_matches_filter(scale):\n",
" \n",
" def get_good_tones(scale):\n",
" good_tones = list(scale.tones)\n",
"\n",
" # Add an upper and lower octave to the list of good known tones. \n",
" for i in range(len(SYSTEMS[\"western\"].tones)):\n",
" good_tones.append(good_tones[i].add(12))\n",
" good_tones.append(good_tones[i].add(-12))\n",
" \n",
" return good_tones\n",
"\n",
" def matches_the_key(tmst):\n",
" # Expand the (tone, mode, scale) tuple. \n",
" tone, mode, other_scale = tmst\n",
"\n",
" trusted = True\n",
" good_tones = get_good_tones(scale)\n",
" \n",
" # Iterate over each tone: \n",
" for tone in other_scale.tones:\n",
"\n",
" # If the tone isn't in a set of known good tones, don't trust it.\n",
" if tone not in good_tones:\n",
" trusted = False\n",
"\n",
" return trusted\n",
" \n",
" return matches_the_key"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "fHqLEp0c-s49",
"colab_type": "code",
"outputId": "43067572-d5f9-4de7-a3eb-1ce5f12fff37",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 211
}
},
"cell_type": "code",
"source": [
"# Here's the good stuff:\n",
"scale = get_scale(tonic=\"A4\", mode=\"minor\")\n",
"\n",
"print(f\"Scales that match A minor:\\n\")\n",
"\n",
"for tmst in filter(get_matches_filter(scale), get_all_scales()):\n",
" tone, mode, other_scale = tmst\n",
" \n",
" # Filter out chromatic scales. \n",
" if len(other_scale.tones) == len(scale.tones):\n",
" print(f\"{tone.name} {mode}: {other_scale}\")"
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"Scales that match A minor:\n",
"\n",
"A minor: <Scale I=A4 II=B4 III=C4 IV=D4 V=E4 VI=F4 VII=G4 VIII=A5>\n",
"A locrian: <Scale I=A4 II=B4 III=C4 IV=D4 V=E4 VI=F4 VII=G4 VIII=A5>\n",
"A mixolydian: <Scale I=A4 II=B4 III=C4 IV=D4 V=E4 VI=F4 VII=G4 VIII=A5>\n",
"B ionian: <Scale I=B4 II=C4 III=D4 IV=E4 V=F4 VI=G4 VII=A5 VIII=B5>\n",
"B aeolian: <Scale I=B4 II=C4 III=D4 IV=E4 V=F4 VI=G4 VII=A5 VIII=B5>\n",
"C major: <Scale I=C4 II=D4 III=E4 IV=F4 V=G4 VI=A5 VII=B5 VIII=C5>\n",
"E dorian: <Scale I=E4 II=F4 III=G4 IV=A5 V=B5 VI=C5 VII=D5 VIII=E5>\n",
"F phrygian: <Scale I=F4 II=G4 III=A5 IV=B5 V=C5 VI=D5 VII=E5 VIII=F5>\n",
"G lydian: <Scale I=G4 II=A5 III=B5 IV=C5 V=D5 VI=E5 VII=F5 VIII=G5>\n"
],
"name": "stdout"
}
]
},
{
"metadata": {
"id": "C8aWpnu98HOh",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"## Playing With Pitch:\n",
"\n",
"PyTheory also supports some advanced pitch exploration:"
]
},
{
"metadata": {
"id": "pfTqnR9I8PpH",
"colab_type": "code",
"outputId": "0680385f-f9a9-4da9-f53e-4fa97054a398",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 35
}
},
"cell_type": "code",
"source": [
"c_min = TonedScale(tonic='C4')['minor']\n",
"c_min"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<Scale I=C4 II=D4 III=D#4 IV=F4 V=G4 VI=G#4 VII=A#5 VIII=C5>"
]
},
"metadata": {
"tags": []
},
"execution_count": 7
}
]
},
{
"metadata": {
"id": "4ccYuYTY8tiW",
"colab_type": "code",
"outputId": "2ad0619a-11c1-4fa2-83eb-6028141f876f",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 35
}
},
"cell_type": "code",
"source": [
"g4 = c_min[\"mixolydian\"]\n",
"g4"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<Tone G4>"
]
},
"metadata": {
"tags": []
},
"execution_count": 8
}
]
},
{
"metadata": {
"id": "c2NXv_-H8t5r",
"colab_type": "code",
"outputId": "fa03752d-15ce-4195-d6f4-dc530e0c21d4",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 35
}
},
"cell_type": "code",
"source": [
"# Rounded decimal.\n",
"g4.pitch()"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"783.990871963499"
]
},
"metadata": {
"tags": []
},
"execution_count": 9
}
]
},
{
"metadata": {
"id": "6VK45wMp9xPy",
"colab_type": "code",
"outputId": "00c403bc-df58-4310-a439-ec5bd481528e",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 35
}
},
"cell_type": "code",
"source": [
"g4.pitch(symbolic=True)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"440*2**(5/6)"
]
},
"metadata": {
"tags": []
},
"execution_count": 10
}
]
},
{
"metadata": {
"id": "Ek1Jj9EA98Hc",
"colab_type": "code",
"outputId": "a03b1ec3-d901-4a91-93e5-fc60f39568da",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 35
}
},
"cell_type": "code",
"source": [
"g4.pitch(temperament=\"pythagorean\", symbolic=True)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"7040/9"
]
},
"metadata": {
"tags": []
},
"execution_count": 11
}
]
}
]
}
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